Scratch preventing metal push belt and oil specification

ABSTRACT

The invention relates to a composite driving belt provided with a carrier and a plurality of transverse elements assembled slidably thereon, the carrier comprising one or more bands, preferably composed of a plurality of endless metal bands disposed radially around each other, each element being provided with a radially outward directed carrier contact plane for contacting a radial inner contact plane of said carrier while in operation, wherein the contacting plane of the transverse element is shaped by an substantially flat surface, while the inner contacting face of the carrier contacting the contact plane the element has a profiled surface, the combined roughness Ra′ of both surfaces being more than 0.6 μm, preferably over 0.75 μm. In particular the roughness and shape of the relevant contacting faces of a belt are adapted to achieve a boundary lubricating condition, while the lubricating oil is defined to meet the requirements of prohibiting the occurrence of scratch, at least reducing the urging thereof considerably.

[0001] The invention relates to a composite driving belt provided with acarrier and a plurality of transverse elements assembled slidablythereon, as described in the preamble of claim 1, the transmissiondefined in claim 7 and to the type of oil defined in claim 8, allrelated to the functioning of the belt.

[0002] Such Belt is generally known, e.g. described in U.S. Pat. Nos.3,720,113 and 4,080,841. In the known belt, a carrier, alternativelydenoted tensile element or tensile means, is composed as a package of anumber of endless metal bands. The known belt may in particular beapplied in a variable transmission, whereby the driving belt runs overpulleys, the substantial conical sheaves of which are adapted to bedisplaced axially relative to each other so that the running diameter ofthe driving belt over the pulley may vary. In turn, while the belt is inoperation, the carrier or band package slides over a contact face, theso-called saddle part of the transverse elements. Also, the separatebands of the package slide relatively to each other during operation.

[0003] In practice the driving belt, in particular each of the bands, isunder a very high tension, on the one hand to ensure a proper frictionalcontact between the pulleys and the transverse elements and on the otherhand to properly conduct the transverse elements in the straight part ofthe driving belt, i.e. to prevent the belt, in particular the transverseelements in the straight trajectory part of the belt from splashingapart.

[0004] The known belts of the current type perform satisfactorily,however may be applied in a transmission environment where thelubrication oil is not of a type optimal for CVT due to standardisationat a manufacturer, may also be applied where mechanical parts are forsake of costs not chosen such that gears are incorporated in anoptimally meshing manner or, alternatively, the gears are incorporatednon-pretensioned in the transmission. Also where costs are saved onisolation of the engine and transmission room, irritating noise mayarise from the drive train of a vehicle and may disturb the driverthereof. The sounds of such noise is known to originate from gear wheelswithin the drive train of the vehicle, rotating impaired duringoperating of a vehicle and is commonly denoted “rattle” or “gearrattle”. Also the term “scratch” is used.

[0005] The present invention seeks to contribute to the solving of suchrattle problem by providing a belt design which is not prone, at leastconsiderably less than the known belt, to urge meshing gear wheels intoa state of vibration causing the rattle. According to the currentinvention such is achieved by applying the measures of thecharacterising portion of claim 1.

[0006] According to an idea and a tribological insight underlying theinvention and considered part thereof, the belt may during operation ofa drive train run in varying conditions, influencing the coefficient offriction in the frictional contact between the carrier of the belt andthe transverse elements thereof. With a belt construction in accordancewith the invention, it is effected in accordance with the tribologicalinsight underlying the invention, that the belt will run in a conditionwhere the coefficient of friction is no longer, at least considerablyless prone to change in operating conditions. In this manner, be it tothe extend of some efficiency loss of the belt performance, the belt maybe incorporated in a drive train with a view to solving the “rattle”problem thereof.

[0007] In particular the roughness of each contacting surface of elementand carrier is produced in such roughness that this factor becomesdominant over other factors influencing the lubrication state. E.g. bythe relatively high peaks which may be recognised in a high Ra valuesurface, the lubricating oil will be influenced such that even at highrelative speeds, or even with a hydrodynamic or full film lubricationpromoting shape of the element contact surface, the oil film in betweenthe contact surfaces will remain of such nature that a boundarylubrication, i.e. with a high coefficient of friction will remain intact for most of the operating conditions, at least for the conditionswhere transmission systems are critical to scratch excitation.

[0008] The latter condition may in accordance with a specific embodimentof the invention further be promoted, by the omission of a wedge shapedentry space between the element contacting face and the carrier, i.e.other than caused by ordinary facet rounding, e.g. realised with thesubstantially flat shape of the saddle part of a transverse element, itis achieved that lubricating oil within the contact between saddlecarrier will only be available to an extend causing so called boundarylubrication. In this lubrication state a relatively constant coefficientof friction occurs. By the shape of the saddle, it is prevented that oilaccumulates before such contact in a manner that an amount of lubricantcausing a mixed or a full hydrodynamic lubrication may enter the actuallocation of contact between carrier and element saddle.

[0009] In a so called mixed lubrication state, also in accordance withan insight underlying and part of the invention, the frictioncoefficient changes with changes in relative speed between carrier andtransverse element. Thus in a further elaboration of the invention thedistance between saddle and the so called mutual rocking edge ofelements within a belt is set lower than 1 mm, preferably the rockingedge is set between 0.4 and 0.8 mm below the saddle. In this manner themaximum relative speed between the element saddle and the carrier ismade lower so that by this measure, the maintenance of a boundarylubrication state is yet further promoted.

[0010] In yet a further embodiment in accordance with the invention, thelubricating oil used in conjunction with the belt is set to a very lowviscosity, preferably as provided in claim 8, thereby impeding thecoming into existence of a boundary or full lubrication state betweenelement and carrier.

[0011] Thus the invention not only relates to a belt and transmissionwith any of the above measures, however, in particular to a belt andtransmission in which the high roughness feature is combined with anyone or more of the above provided set of measures.

[0012] The boundary lubrication state is in accordance with theinvention preferred over the hydrodynamic lubrication state of operationof the belt since it was established by the investigations underlyingthe invention that the relative speeds within a belt running in atransmission, may drop to zero so that the HL lubrication condition cannot in all operating conditions be maintained. Rather the frictioncoefficient appears to change from relatively low to relatively highwith relative speed within the belt, i.e. amongst others with theinstantaneous transmission ratio of the belt, together with thelubrication state in the belt which appears to dynamically shift from ahydrodynamic lubrication state, via a mixed lubrication state to aboundary lubrication state and vice versa. Thus, in accordance with afurther aspect the belt is designed such, in particular is provided withsuch a roughness that, at least in the LOW transmission mode, theboundary lubrication state will remain, at least the coefficient offriction remains virtually constant over a considerable range of primaryshaft revolutions when the belt is applied in a transmission. The LOWtransmission state is in accordance with further insight underlying thetransmission preferred over the OD state where also extreme relativespeed differences may occur in the belt, since it is recognised thatmost transmission systems feature less vulnerability for scratch in thisa transmission mode.

[0013] The invention will now further be explained further by way ofexample along a drawing in which:

[0014]FIG. 1 represents a single ring of prior art belt, adapted inroughness in accordance with the present invention;

[0015]FIG. 2 is a tribological graph for the belt realised by researchunderlying the invention, and providing the insight upon which theinvention is based;

[0016]FIG. 3 is a schematic representation of an insight underlying thepresent invention, abstractly reconsidering the components of a belt inanalogy to frictional physics;

[0017]FIG. 4 represents a radial cross section of a belt, showing atransverse element and the tensile means cross section

[0018]FIG. 5 is a cross section of the transverse element along the lineB-B in FIG. 4, while

[0019]FIG. 6 more in detail provides the cross section of the so-calledsaddle part in FIG. 5, to be applied in accordance with the invention ata defined roughness, preferably in combination with the carrier part ofFIG. 1;

[0020]FIG. 7 is a displacement graph of a block m of the model inaccordance with FIG. 3, as a function of time during stick-slipbehaviour;

[0021]FIG. 8 is a schematic illustration of the interaction between apush belt transmission and meshing gear wheels of a drive train.

[0022]FIG. 9 is a representation of characteristic belt and transmissionfeature realised by the invention.

[0023] In the figures corresponding components are denoted by identicalreferences.

[0024]FIG. 1 represents a ring of a drive belt, in particular push beltas commonly known. The ring may be part of a carrier of form the same,however is in common applications like automotive personal vehicle andtrucks, utilised in a nested arrangement of a plurality ofcircumscribing loops or rings, as may e.g. be taken from FIG. 4. Such aset of nested rings forms part or all of the belt's tensile means alongwhich transverse elements are disposed freely moveable in the endlesslongitudinal direction of the belt. The elements are clamped between thesheaves of a set of pulleys and transmit rotation from one drive pulleyto a driven pulley. The tensile means thereby serves to keep togetherthe transverse elements pushing against each other. In the presentexample both the transverse elements and the tensile means are composedof a metal.

[0025] When the driving belt runs over pulleys having different runningdiameters, the variable bands of the band package have a mutual speeddifference, at least in situ of one of the pulleys. This speeddifference may in practice be more than 0.4 meter per second between twosuccessive bands disposed around each other. Moreover, notably the innerbands of a carrier are pressed on to each other with substantial force,since the pressure force on a band is built up by all bands disposedoutside i.e. there around.

[0026] By providing in particular the more inwardly disposed bands atleast at one side with a surface profiling, through which an improvedlubrication between the bands will be produced, less wear and increasedlife time is promoted. Preferably, the surface profiling comprisesgrooves, which in practice provide good results. According to a furtherfeature, the roughening value of the surface profiling lies between 0.30and 0.75 μm Ra, here measured according to CLA method, and preferablybetween 0.46 end 0.55 μm Ra. In a preferred embodiment the roughness isachieved by grooves disposed in crossing sets. The grooved profiling ofa metal band is achieved by rolling a band between rollers, one rollerbeing fitted with a surface profiling on the circumferential surface.

[0027] The drawing in FIG. 1 diagrammatically shows an endless metalband. The width of such a band may e.g. range between 5 and 20 mm andthe thickness between 0.15 end 0.25 mm. The diameter of the band incircular condition may e.g. range between 150 and 400 mm. The endlessband has an exterior side 1 and an interior side 2. In the knownembodiment of FIG. 1, the interior side 2 is provided with a surfaceprofiling of crosswise disposed grooves. According to a preferredembodiment of the invention all rings of a belt's tensile means areincorporated in this manner.

[0028] It is further derived from the investigations underlying thecurrent invention that for achieving an anti-scratch adapted belt aspecific, combined set of measures related to the manner of contact andthe lubrication of the contact between a carrier face and the saddle isrequired. According to this set of measures, for lubrication of thiscontact, it should be promoted that a restricted amount of lubrication,i.e. oil occurs between element and carrier, the so called boundarylubrication, in combination with a relatively very much roughenedsurface area of both contacting faces, i.e. saddle face and the innerband facing of a carrier in order to prevent separation, ergo tomaintain bounding lubrication. According to the invention, primarily,the smoothening, expressed in roughness parameter Ra, of both facesshould be such that the so-called reduced roughness Ra′, i.e.

Ra′=SQRT (Ras ² +Rar ²)  (1)

[0029] In which

[0030] Ra′=the combined roughness parameter

[0031] Ras=the average roughness parameter of the saddle surfaceexpressed in Ra.

[0032] Rar=the parameter for the average roughness of the inner ringface contacting the saddle.

[0033] SQRT=square root of ( . . . )

[0034] meets the requirement to be greater than 0.6 μm, preferably toremain within the area over than 0.75 μm.

[0035]FIG. 2 diagrammatically reflects a curved typical relationaccording to the invention between a friction coefficient or parameter,linearly parameterised along the Y-axis of the figure, and a “belt andoil features” parameter L, alternatively Lubrication number L,logarithmically expressed along the X-axis. The parameter L iscalculated utilising the dimensionless number $\begin{matrix}{L = \frac{\eta_{0}V_{r}}{p_{a\quad v}R_{a}}} & (2)\end{matrix}$

[0036] in which:

[0037] L=a lubrication number or parameter in accordance with an insightunderlying the invention;

[0038] Vr=the relative speed between the two contacting surfaces, hereof the inner belt ring and a transverse element's saddle;

[0039] η₀=the dynamic viscosity parameter of the lubricating medium atambient pressure;

[0040] Pav=the average Herzian stress within the band/saddle contact;

[0041] Ra=the combined surface roughness Ra′ of both saddle and ringsurface.

[0042] The combined surface roughness Ra′ is calculated in the ordinarymanner in the art provided above, and expressed in roughness coefficientRa′.

[0043] The principal characteristic of the curved relation given byformula 1 and FIG. 3 is according to the invention determined bydominant parameters Vr, and Ra, whereas the viscosity and the averageHertzian pressure parameters are in accordance with the insightaccording to the invention not, at least not directly related to designparameters of the belt. The lubrication number L equation (2) accordingto the invention more in particular reveals that relative speed Vr isthe most dominant factor for influencing the friction coefficient due tochanging operation conditions, since also Ra is given once the belt isset into operation.

[0044]FIG. 2 shows in accordance with experimental results of researchunderlying the invention and matching the parameter line depicted inFIG. 2, that the relation between an actual friction coefficient and thelubrication parameter appears to typically follow a curve with threemain sections. In the first section BL, suggestedly where so calledboundary lubrication, i.e. shearing contact exists between the twocontacting surfaces, the friction coefficient is virtually constant withincreasing parameter L. In a second section ML, suggestedly where mixedlubrication and friction occurs, the friction coefficient drops withincreasing L number, typically from somewhere like 0.16 to somewherelike 0.01. In the third section HL, where suggestedly hydrodynamiclubrication exists, i.e. with shear occurring within the lubricant andnot between the contacting surfaces, the actual friction parameter hasit's lowest value and again is virtually constant or may slightlyincrease again with increasing value of L. This section may moreaccurately also be denoted elasto hydrodynamic lubrication EHL.

[0045]FIG. 4 provides a cross section of a belt and a view of atransverse element, depicted according to a view in the longitudinaldirection of the belt. FIG. 5 is a transverse cross section thereof overthe line B-B, with the tensile means being omitted from the drawing,providing a view in a belt's axial direction. FIG. 6 in an enlargedscale depicts the in FIG. 5 encircled part of the element, in fact thepart which contacts the inner face of a belts tensile means, the socalled saddle of an element. In this element the roughness Ra is a partof a set of measures increased considerably over the roughness value ofknown commercialised belts, including an increase in roughness of thecarrier.

[0046] It is a further prerequisite in accordance with the inventionthat for achieving the desired condition in the mutual contact, thelocal bending radius Rb of the band, i.e. tensile means, and of thesaddle Rs should preferably be equal, thus:

Rb=Rs  (4a)

[0047] Since this requirement in the practise of an operating belt cannot be achieved, the design in accordance with the invention should atleast fulfil that:

Rs>Rb  (4b)

[0048] In accordance with a further aspect underlying the invention, thecombined local radius, i.e. the reduced radius of both the saddle andthe tensile means is taken into consideration by the requirement:

1/Rr=1/Rs+1/Rb  (5)

[0049] in which

[0050] Rr=the reduced radius of a Carrier and Saddle face contact

[0051] Rs=the local radius of the saddle measured in mm

[0052] Rb=the instantaneous radius of the band measured in mm

[0053] It is in accordance with the invention considered that for mostapplications of a belt, generally Rs should range over 80 mm, whereas,whereas Rb for commonly applied transmissions typically ranges between25 and 80 mm during operation of the Belt. For preventing that oilaccumulates in the contact between carrier to an amount causing thedescribed ML and HL lubricating conditions the element is shaped so asto avoid a wedge shaped spacing between carrier and saddle (like e.g.present in the embodiment according to FIG. 6. Since the running radiusof the belt varies with the transfer ratio of the transmission, flat isdefined such that any possible concave shape in the cross section of thesaddle should be of a radius substantially higher than the largestrunning radius specified for the belt or occurring within a transmissionin which the belt is to be incorporated.

[0054] Both radii are taken in accordance with the radial andlongitudinal direction of a belt, considering the normal operation andconfiguration thereof in a pulley. More in particular it is consideredthat for obviating the said wedge shaped entry space at the largestamount of possible contacting locations on a saddle, without preferablythe radii of saddle and band becoming equal, the saddle is preferablyshaped with a non-continuous i.e. edged transition in a possiblecontacting surface, since from experience underlying the invention it isknown that these will break, i.e. remove the lubricated condition in themutual contact.

[0055] For even better performance of a belt and transmission inaccordance with the invention, the invention provides to apply alubricating medium in the form of an oil type having a dynamic viscosityη lower or equal to 4 MPa*s at a nominal temperature of 100 degreesCelsius. In this manner “L” is reduced further, so that the change inlubrication condition from the BL area to the ML area in the graph isshifted to the left, i.e. the ML is even further reduced. By applyingall or a majority of the different measures of the set provided by thisinvention the operation of a belt is optimised, for solving a scratchproblem of a transmission.

[0056] In the latter respect, according to an even further aspect of theinvention and preferably taken into account in the set of specificmeasures in accordance with the invention, the so-called rocking edge ofthe belt is provided less than 1 mm from the saddle surface, more inparticular in a range between 0.4 and 0.8 mm below the saddle surface.In this manner it is achieved to decrease the relative velocity Vrbetween saddle and tensile means, alternatively denoted carrier, inparticular at the extreme OD and LOW ends of the range of ratios inwhich the belt will operate. In combination with any, preferably all ofthe previous measures this measure appears to diminish the occurrence ofso called rattle in a transmission, at least the transmission appears tobecome less prone to being urged into such state, be it to the expenseof some loss of efficiency in performance of the belt, in particular inthe LOW and OD areas of the belt's range of transmission ratios.

[0057]FIG. 3 illustrates a mathematical model taken into considerationand developed at developing the insight underlying the claimedinvention, of the friction occurring within the belt. In the model, itshows that changing the friction force F_(w)=μF_(N), will lead tochanges in the spring force F_(s)=kx, which may lead to vibrations ifthe damping force (F_(d)=c{dot over (x)}) is not sufficient. It has beendistinguished between dynamic frictional behaviour due to externalexcitation and self (or internal) excitation. The value for the frictionforce F_(W) is in this model interchanged with a result of two factors:coefficient of friction μ and normal force F_(N) (considered thatF_(w)=μF_(N)). The external form can lead to vibrations due to a(periodical) change in normal force, e.g. F_(N)(t)=sin(ωt). For examplethe pressure fluctuations in the pulleys will lead to a change in normalforce with time in the contact between saddle and ring in the CVT.

[0058] Attention will now be paid to the self or internal excitationform, which in accordance with the idea underlying the invention, maylead to vibrations due to a change in coefficient of friction withrelative velocity.

[0059] In case of self excitation ‘Classical’ stick-slip, where thecoefficient of friction changes when going from static to kineticfriction, is distinguished, as well as Stick-slip-related, orμ_(k)−V_(r) dependent behaviour, where in a system already in motion(only slip) the kinetic coefficient of friction changes with relativevelocity V_(r).

[0060] Classical stick-slip arises when the coefficient of staticfriction is greater than the coefficient of kinetic friction. In themodel of FIG. 3, the block with mass m will stick to the lower surfaceif the coefficient of friction is sufficiently large at the equilibriumposition when moving it along with an absolute velocity of value {dotover (x)}=V. During the stick period the force relationship may bewritten as

cV+kx<μ _(s) F _(N)  (6)

[0061] During the stick, the spring force increases with time at a ratekVt (or kx) as the slider is displaced from point A to point B asindicated in FIG. 7. Up to point B, the static friction force is capableof withstanding the combined restoring forces consisting of the constantdamping force cV and the increasing spring force kx. At point B, therestoring forces overcome the static friction force μ_(s)F_(N) and slipoccurs to point C.

[0062] Considering the slip-phase the motion of the mass or block “m inFIG. 3 is described by the equation

m{umlaut over (x)}+c{dot over (x)}+kx=μ _(k) F _(N)  (7)

[0063] It is assumed that at a certain moment μ_(k) decreases withincreasing relative velocity V_(r) according to hydrodynamic actioneffects in the lubricated contact. For the moment only the dependency ofμ_(k) with V_(r) is considered. An extension to other parameters ofinfluence, important for design recommendations, will be given furtheron.

[0064] As a first approximation the dependency of μ_(k) with V_(r) canbe modelled by a linear relationship with a certain negative slope (α)according to

μ_(k)=μ_(k) ⁰ −αV _(r)  (8)

[0065] The expression (8) for μ_(k) can be substituted in equation (7),with

V _(r) =V−{dot over (x)}  (9)

[0066] which yields the following equation

m{umlaut over (x)}+( c−αF _(N)){dot over (x)}+kx=(μ_(k) ⁰ −αV)F_(N)  (10)

[0067] In accordance with the insight underlying the invention, theslope α has been introduced in the damping term. Here it acts in anegative way. A negative damping coefficient feeds energy into thesystem and makes vibrations and even resonance possible. It is thusdemonstrated by the development underlying the current invention thatwhen the resulting amplitudes and frequencies match certain criticalsystem characteristics of the gear set gear rattle will occur.

[0068] It is also demonstrated that unlike what quite often is assumed,stick is not a necessary condition for the occurrence of rotationalvibrations. Rather the behaviour of the change in coefficient offriction with velocity may lead to these vibrations. Furthermore itshould be noticed that any disturbance in the transmission may lead toexcitation of the mass-spring-damper-friction system due to the inherentunstable nature of this system.

[0069] Further in accordance with the idea underlying the invention, themass-spring-damper-friction model is applied to the push belt/variator,at which, e.g. in Low, the following simplification is made regardingthe belt and transmission as shown in modelled FIG. 8. In the dynamicalsystem of the variator only relative motion between saddle and ring, assource, and vibrations of the secondary axis in the variator, as effect,are considered. The absolute movement of a stating belt is here nottaken into consideration since, in accordance with the insightunderlying the invention it does not play a role in triggeringtransmission scratch.

[0070] The mass, in particular the vibrating mass in the model accordingto FIG. 8 is represented by the secondary axis in the transmissionaccording to the invention. The element string constitutes the springwhen the stiffness is considered and also plays a damping role. Theelement string will be formed by different elements in time due to thedynamic nature of the system. Two situations can be distinguished. Thefirst situation is defined in that the element string is not loaded in away that compressive forces are able to overcome the endplay (theso-called ‘lose part’). The second situation is when there is no play,i.e. end play, in the belt anymore, which is the case in the ‘push part’occurring during operation of the belt. According to the firstsituation, when there is some amount of endplay in the element string,this part, which is considered to feature certain stiffness and damping,does not have to be taken into account. However in the second situation,when there is no endplay, this part, having a characteristic stiffnessand damping, is however considered in the model developed in accordancewith the ideas underlying the invention.

[0071] Friction occurs between the saddle and ring on the primarypulley. The normal force in this contact is the parameter F_(N) used inthe model. The ring is moving relatively to the elements in the primarypulley with a certain relative velocity V. The overall relative velocityVr, i.e. V superimposed with vibration {dot over (x)}, which is crucialfor the frictional behaviour, is according to equation (9).

[0072] At applying the developed model to predict the amplitudes andfrequencies of vibration, it is considered that the gears limit thisvibration form by means of the play that exists between the teeth of thegears pertaining to a transmission according to the invention. Therefortwo situations are distinguished. First, if the amplitude of vibrationis greater than the play between the gear teeth, gear rattle may occurtwo sided. Second, if this amplitude is smaller then gear rattle mayoccur single sided.

[0073] The gear set as shown in FIG. 8 is only for illustrativepurposes. It will be explained using the model described along FIG. 3,while the individual effects of changes in the governing operationalvariables are in accordance with the invention identified. The followingvariables are identified:

[0074] m—mass of the secondary axis

[0075] c—damping coefficient

[0076] k—spring stiffness of the element string

[0077] F_(N)—normal force in the saddle-ring contact

[0078] μ_(k)—kinetic coefficient of friction dependent of the tribologyin the saddle-ring contact

[0079] The combination of the items mentioned above is responsible forthe system behaviour regarding rotational vibration. The last item,which concerns the influence of tribology aspects on the kineticcoefficient of friction, has been paid special attention to. In thelubricated saddle-ring contact the coefficient of friction is a dynamicparameter depending on variables like relative velocity, viscosity,temperature, pressure and roughness.

[0080] Another important parameter is the play between the elements. Ifthere is some amount of play, e.g. in case of the so called ‘lose part’of a belt operating in a transmission and when the amplitude of thevibration is not exceeding the play, the stiffness and damping of thispart do not have to be taken into account. Then only the stiffness anddamping of the push part have to be considered.

[0081] The dynamic behaviour of the coefficient of friction isrepresented in the tribological curve for the push belt (FIG. 2). Inthis curve the coefficient of friction is mapped as a function of thedimensionless number L defined by equation (2), utilising the combinedroughness defined in equation (1).

[0082] In equation (11), the lubrication number L is incorporated,instead of only in the motion equation. This yields $\begin{matrix}{{{m\quad \overset{¨}{x}} + {\underset{\underset{1}{}}{( {c - {\frac{{\alpha\eta}_{0}}{p_{a\quad v}R_{a}}F_{N}}} )}\overset{.}{x}} + {k\quad x}} = {\underset{\underset{2}{}}{( {\mu_{k}^{0} - {\frac{{\alpha\eta}_{0}}{p_{a\quad v}R_{a}}V}} )}F_{N}}} & (11)\end{matrix}$

[0083] Equation (11) shows two counteracting terms when vibration isconcerned. The equation makes clear that the amplitude of vibrationincreases if term 1 decreases and/or term 2 of equation (11) increases.Therefore the parameters in term$\frac{{\alpha\eta}_{0}}{p_{a\quad v}R_{a}}$

[0084] have both a positive and negative effect on the amplitude. Thenet result follows from the governing system parameters.

[0085] In the above representation of the tribological curve for thebelt, the hydrodynamic action of the contact is assumed. I.e. increasein hydrodynamic separation, i.e. film thickness over roughness, leads toa decrease in the coefficient of friction, i.e. leads to a shift from aboundary lubrication state (BL) to a mixed lubrication state (ML) forlow values of L and assuming that friction is constant in the boundarylubrication regime. In FIG. 9 it illustrates that with at least aplurality of the measures of the set provided by the invention, a highcoefficient of friction is maintained for a considerable part of acommon range of rotational speeds of the primary shaft. The belt herebyruns in a LOW transmission ratio, which appeared the most scratchtriggering transmission mode. The belt feature illustrated in this graphcomprises that the friction coefficient remains virtually constant, i.e.does not decrease more than about 10% up to a predetermined value of thespeed of the primary shaft, here over a major part of the transmissionsregular range of transmission ratios. In this FIG. 9 the dotted lineillustrates the dependency of the coefficient of friction without any ofthe measures according to the invention being taken.

[0086] In a preferred embodiment of the invention so much of the set ofmeasures is applied such that the critical constant high value of thefriction coefficient is maintained up to a primary speed value of 4000RPM, More preferably however, this state is maintained in the said LOWtransmission mode up to 6000 RPM.

[0087] The invention further relates to all details of the figurespertaining to the description and all features defined in the followingclaims.

1. A composite driving belt provided with a carrier and a plurality oftransverse elements assembled freely slidable thereon, the carriercomprising one or more bands, preferably a plurality of endless metalbands, disposed radially around each other, each element being providedwith a radially outward directed carrier contact plane for contacting aradial inner contact plane of said carrier while in operation,characterised in that the carrier contacting face of the transverseelement and the inner contacting face of the carrier contacting thecontact face the element have a combined roughness Ra′ that is more than0.6 μm, preferably over 0.75 μm.
 2. Belt according to claim 1,characterised in that the roughness Ra of the carrier inner inwardfacing (2) is larger than Ra 0.8.
 3. Belt according to claim 1 or 2,characterised in that the surface profiling is realised by groovesdisposed in crossing sets.
 4. Belt according to claim 3 or 4,characterised in that the shape of the carrier contacting face of thetransverse element, taken in cross section thereof and in the beltlongitudinal direction, corresponds to a radius of curvaturesubstantially preferably larger than the largest running radiusspecified for the belt.
 5. Belt according to any of the precedingclaims, characterised in that the carrier contacting face of the elementis shaped by a substantially flat surface.
 6. Belt according to any ofthe preceding claims, characterised in that the rocking edge of atransverse element is set less than 1 mm below the saddle surface. 7.Belt according to claim 6, characterised in that the rocking edge islocated in a range between 0.4 and 0.8 mm below the saddle surface. 8.Transmission provided with a belt according to any of the precedingclaims, in which the belt operates under lubricated conditions providedby a lubricating oil, characterised in that the lubricating oil has adynamic viscosity η lower or equal to 4 MPa*s, at a nominal temperatureof 100 degrees Celsius.
 9. Lubricating oil for use in a continuouslyvariable transmission type transmission having the features of claim 8.10. Transmission including a belt according to claim 1 in which at leastone of a remainder of a set of measures provided by the claims 2 to 8 isprovided, such that when the belt is operated in a LOW mode oftransmission, the friction coefficient between the carrier and anelement remains at least virtually constant over a major part of theregular range of primary shaft rotation speeds to be transmitted,preferably up to 4000 RPM, more preferably up to 6000 RPM.